Remark that the matrix is symmetric, stochastic and hence have real eigenvalues, the largest one being equal to . Nevertheless, a multigraph is not reconstructible from this distance as replacing every edge by parallel edges does not affect the distances between the vertices.
#define SEUIL 0.00001 |
Threshold for clustering optimization termination.
Clustering optimization process is repeated until the inertia is modified by less than SEUIL
int diag | ( | double ** | dis, | |
int | NumberOfPoints, | |||
double ** | Distances, | |||
svector< double > & | EigenValues, | |||
bool | project | |||
) |
Isometrically embed a set of points with given distances among them in the Euclidean space .
dis | coordinates of the points (returned value) | |
NumberOfPoints | number of points > 2 | |
Distances | distances among the points | |
EigenValues | eigenvalues of dis (returned value) | |
project | indicates if one should project the matrix of distances before putting it in diagonal form (always true except when using the Laplacian) |
Distances
matrix into the dis
matrix, dis
to be put in diagonal form dis
dis
int& useDistance | ( | ) |